design of zero dispersion optical fiber at wavelength 1.3 m

J. Edu. & Sci., Vol. (27 ), No. (4) 2018

54

Design of Zero Dispersion Optical Fiber

at Wavelength 1.3 m

R.S. Habeb Physics department, College of Education,

Mosel University

Accepted Received

06/03/2013 25/09/2012

الخلاصةايك و ممم3,1) عشمما ب لمم م ب سمم ه بتقمم ص رمم فممه امملب ب تحممم ترممسو ومم مم هتمم

, ( كوب مادة ب لو , معاممل بلاكسدما ت ,ب سقلع ب ع هواه ) بالاعتساد على عاة ع بمل مت (فمه كمسمة كتوم بذمكلاله ب ع بمل يجب بختوا اا باقة عشما ترمسو وم م ه لاكؤما تم

.لوبوشت ب سحاكاة بعض ب سسو بت ب ؤامة وب ودوة ب ستعلقة بؤلب ب ع بم بلاترالات ب ز وةكم يمممما %( 3.1بشدممممتة ) لقلممممب (GeO2) ملعممم بممممم ومممم مممم ه ب حرمممم م علمممىتممم

وب قو ب سثلى سعامل بلاكسدا سل من قلب ب لو وغلافه (OptiFiber2.0) باستخابم ب ت كامج( وب مممل يدمممتعسل فمممه ممممايك ومت 3,1لأ مممل ب حرممم م علمممى تقممم ص رممم عشممما ب لممم م ب سممم ه )

( معممام ب مم ن بممون ب سعمماملون 3,23و 3,26ت علممى ب تمم ب ه )كاكمموقمما .بلاترممالات ب زمم وة .مت ( على ب ت ب همايك و 6,24و 4,506بأكراف قلا ) (0%...)

Abstract:

In this article, an optical fiber was designed with zero- dispersion at

wavelength of (1.3 m). The design took into consideration many factors

of the fiber, such as; fiber cross- section, fiber material, refractive index.

These factor can affect the operation of a fiber in optical communication

system.

A zero- dispersion fiber was obtained when the core was doped by

(1.3%) of GeO2. Implementing the package of computer aided design

(OptiFiber 2.0). We were able to attain the optimum values for refractive

index core and clad as (1.48 and 1.45) respectively, i.e, a percentage

difference of (0.02) for radius (6.728 and 8.46) respectively, for zero-

dispersion at wavelength of (1.3 m) that is use in the optical

communication.

Design of Zero Dispersion Optical Fiber at Wavelength 1.3 m

55

1. Introduction Telecommunications using fibers as the transmission media is now

a major industry[1]. Optical fiber technology was considered to be a

major driver behind the information technology revolution and the huge

progress on global telecommunications that has been witnessed in recent

years. Fiber optic telecommunication is now taken for granted in view of

its wide-ranging application as the most suitable singular transmission

medium for voice, video, and data signals[ 2]. Indeed, optical fibers have

now penetrated virtually all segments of telecommunication networks;

trans-oceanic, transcontinental, inter-city, metro, access, campus, or on-

premise [2].

The role of a communication channel is to transport the optical

signal from transmitter to receiver without distorting it. Most light wave

systems use optical fibers as the communication channel because silica

fibers can transmit light with losses as small as (0.2 dB/km). Even then,

optical power reduces to only (1%) after (100 km)[3]. For this reason,

fiber losses remain an important design issue and determines the repeater

or amplifier spacing of a long-haul light wave system [3]. Another

important design issue is fiber dispersion, which leads to broadening of

individual optical pulses with propagation. If optical pulses spread

significantly outside their allocated bit slot, the transmitted signal is

severely degraded. Eventually, it becomes impossible to recover the

original signal with high accuracy[3]. The problem is most severe in the

case of multimode fibers, since pulses spread rapidly (typically at a rate

of 10 ns/km) because of different speeds associated with different fiber

modes[3]. It is for this reason that most optical communication systems

use single-mode fibers. Material dispersion (related to the frequency

dependence of the refractive index) still leads to pulse broadening

(typically<0.1 ns/km), but it is small enough to be acceptable for most

applications and can be reduced further by controlling the spectral width

of the optical source[3]. material dispersion sets the ultimate limit on the

bit rate and the transmission distance of fiber-optic communication

systems[3].

Dispersion is sometimes called chromatic dispersion to emphasize

its wavelength-dependent nature, or Group Velocity Dispersion (GVD) to

emphasize the role of the group velocity[4].

The group velocity associated with the fundamental mode is frequency

dependent because of chromatic dispersion. As a result, different spectral

components of the pulse travel at slightly different group velocities, a

phenomenon referred to as group-velocity dispersion (GVD), intramodal

dispersion, or simply fiber dispersion. Intramodal dispersion has two

R.S. Habeb

56

contributions, material dispersion and waveguide dispersion. We consider

both of them and discuss how GVD limits the performance of light wave

systems employing single-mode fibers[3].

Dispersion represents a broad class of phenomena related to the

fact that the velocity of the electromagnetic wave depends on the

wavelength. In telecommunication the term of dispersion is used to

describe the processes which cause that the signal carried by the

electromagnetic wave and propagating in an optical fiber is degradated as

a result of the dispersion phenomena. This degradation occurs because the

different components of radiation having different frequencies propagate

with different velocities[6].

The different velocities of the two orthogonal components generate

the phase difference changing in time of propagation along a fiber and

change of polarization. Beside the change of polarization with time of

propagation, the different velocities of ordinary ray and extraordinary

cause that the rays reach the end of a fiber in different time[7].

(OptiFiber) is the leading commercial product in that category. It is

a powerful tool that blends numerical mode solvers for fiber modes with

calculation models for group delay, group-velocity dispersion, effective

mode area, losses, polarization mode dispersion, effective nonlinearity,

etc[1].

In this article, a fiber design was intended in order to obtain a

Zero_ dispersion fiber operating in the wavelength of (1.3 m). The

design was implemented by using (OptiFiber 2.0) and solving filed

equation by (MATLAB). Comparison will be stated in the article .

2. Fiber geometry and numerical method

The optical properties of the fabricated fibers are assessed both

experimentally and through accurate numerical simulations. The second

key, optical property of a fiber, is its dispersion profile, which

characterizes the wavelength dependence of the group velocity(vg) of the

guided mode[8].

Consider a single-mode fiber of wavelength (). The fiber group

index (ng) is related to the first order derivative of the mode propagation

constant (β) with respect to (λ) according to the following expression[8],

we have:

)1....(....................

)dc2π

λ(

dβ

2π

λ

gn

2

2


57

By Taylor expression around resonance frequency(ω0), (β) can be

written[5]:

)(2....................)0

ω(ω2

β2

1)

0ω(ω

1β

0ββ

With: 0

ωω)

2dω

β2d(

2β,

0ωω

)dw

dβ(

1β

using k = 2π/λ, equation (1) can be written as[8]:

)3.....(..............................)dλ

dβ(

gn c

By using equation (3), (vg) is[7]:

)4.....(..............................n

cv

g

g

Dispersion is also related to (neff) which given as[9]:

)5....(....................dλ

nd

cD

2

eff

2

(neff) is an effective index of the fundamental mode in a single-mode

fiber, and (c) is speed of light in the vacuum.

In a fiber, the materials of core and cladding are of different

refractive indices. If there are (I) layers in the fiber cross-section, each

layer has different refractive index. If the refractive index of the fiber

material varies with wavelength, thus causing the group velocity to vary,

it is classified as material dispersion[9].

The total material dispersion of a fiber in term of variation of with

respect to wave length, we have[3]:

)6......(....................dλ

dn

c

1

MD

g

And waveguide dispersion is the result of the wavelength-

dependence of the effective refractive index (neff) of the fiber mode. First,

the mode solver calculates the relation between (neff)and wavelength (λ),

then the waveguide dispersion is calculated by[1]:

)7.........(..........dλ

effnd

λc

β

wD

2

2

The total dispersion is the total effect of material and waveguide

dispersion. It is calculated in a similar way as for calculating waveguide

dispersion. In this case, the fiber refractive index profile depends on the

wavelength. The material dispersion effect should be calculated first.

Then the mode solver calculates the mode effective index (neff)[1].

R.S. Habeb

58

It can be shown that the total dispersion coefficient of a fiber (DT)

is given to a very good accuracy by the algebraic sum of two components

which is[9] :

For a double-layered optical fiber structure composed of GeO2 -

doped silica core and pure silica cladding, the acoustic modes have been

theoretically analyzed solving the electric filed equation which Is given

By[10]:

aρ;z)βexp(i)φmexp(i)ρq(m

kC

E

aρ;z)βexp(iφ)mexp(i ρ) (pm

JA

………….(9)

Where (m) is the number of mode, ()the phase of mode, (a) core

radius, (Jm) and (km) are different kinds of Bessel functions and () is

parameter taken as function of (a) [11]. The parameters (p) and (q) are

defined by[3]:

(10)..............................βk

inp

(11)..............................ρk

inq

It was clear during the 1970s that the repeater spacing could be

increased considerably by operating the lightwave system in the

wavelength region near 1.3 m, where fiber loss is below (1 dB/km).

Furthermore, optical fibers exhibit minimum dispersion in this

wavelength region. This realization led to a worldwide effort for the

development of (InGaAsP) semiconductor lasers and detectors operating

near 1.3m [3].

There is currently a great deal of interest in the development of

efficient 1.3 m optical amplifiers, because most terrestrial optical fiber

communication systems work at this wavelength[12].

For the last two decades, varieties of optical fibers have been

developed for optical communications in order to cope with ever

increasing bandwidth, data rate, and transmission distance[13].

Conventional optical fibers consist of a solid glass core with higher

refractive index encircled by cladding with a relatively lower refractive

index. There are three major transmission optical fibers; single-mode

fibers (SMFs), nonzero dispersion shifted fibers (NZDSF), and dispersion

.(8)....................w

DM

DT

D


59

compensating fiber (DCF). With recent worldwide demand in the end of

the 20th century, these silica based conventional fibers have been

massively developed and deployed to obtain larger communication

capacity by optimization of the chromatic dispersion at the S, C, and L-

bands for the wavelength (1.55 m) [13]. Along side with these

transmission fibers, specialty fibers such as rare earth-doped fibers,

photosensitive fibers, attenuation fibers, and polarization maintaining

fibers have been also developed for optical devices[13]. These fibers,

however, do have the common platform as transmission fibers in a sense

that they do share the solid glass core/cladding structures [13]. Optical

communication working at (1.3 m) is in the O band region .

To design a fiber with zero dispersion, it is necessary to optimize

both: material properties, as well as the shape of the waveguide. There

exists, therefore, a wavelength, at which total dispersion is equal to zero.

Beyond this, the fiber exhibits a region of anomalous dispersion, which

can be used for the compression of pulses in optical fibers [14] .

The design of fiber-optic communication systems requires a clear

understanding of the limitations imposed by the loss, dispersion, and

nonlinearity of the fiber. Since fiber properties are wavelength dependent,

the choice of operating wavelength is a major design issue [5].

Step index fiber modeling process is carried out through

numerically solving of eigen value equation to calculate propagation

constant for fundamental mod. Input data in the process is only index of

refraction calculated from Sellmeier dispersive formula for appropriate

mol percentage doping of germanium dioxide in silica glass fiber. Output

data in the modeling process is optimal value of the normalized

frequency, which guarantees that single mode operation region is equal to

bright soliton propagation region. Final verification of the process is

soliton generation up to six-order inside such modeled fiber. In this end

nonlinear Schodinger equation is solved numerically for initial condition

of hyperbolic secant form of laser pulse. Maximization of single mode

operation and bright soliton propagation region is essential in wavelength

division multiplexing technique [15]

The refractive - index relationship with the wavelength and the

concentration is given by Sellmeier equation as [16]:

)12.....(....................k

1i bλ

λi

a1n

2

i

2

2

2

where (k) equal to (3), represents that this is a three term

Sellmeier’s, equation, () is in a unit of micron, (i) is the oscillator

R.S. Habeb

60

resonance wavelength. In this equation, a certain set of parameters (ai)

and (bi ) are corresponding to a specific type of material such as pure

silica or GeO2-doped silica glass with a certain GeO2 concentration level.

A series of (ai) and (bi) have been computed from the measured data

taken from reference, as shown in Table (1). All the parameters of optical

fibers were kept same except for the core radius. The inner cladding

radius was (6.728 m), and the relative refractive index difference

between the core and the cladding was of (2%) similar to that of

conventional SMFs.

Table (1) Sellmeier coefficients values [ 17] :

parameter 96.9 %

SiO2

3.1 %

GeO2

a1 0.6961663 0.7028554

a2 0.4079426 0.4146307

a3 0.89749794 0.8974540

b1(m) 0.068043 0.0727723

b2(m) 0.1162414 0.1143085

b3(m) 9.896161 9.896161

Opti-Fibers code used to simulate the micro-fiber. The commercial

single mode optical fiber parameters with dimensions squeezed were

chosen for simulation. As at a very narrow core size, silica is the

dominating factor rather than GeO2 to determine the propagation

characteristics, the core itself was approximated to be of silica glass.

3. Results and discussion

Figure (1) displays how the refractive index (n) and the group

index (ng) varies with wavelength for fused silica. The group velocity can

be found using equation (4) by (MATLAB). Physically speaking, the

envelope of an optical pulse moves at the group velocity[6].


61

Figure (1): Variation of (n) and (ng) with wavelength

The wavelength dependence of (n) and (n g ) in the range (0.5–2

µm ) for fused silica. Material dispersion (DM ) is related to the slope of

(n g )by the relation[Eq. (6)]. It turns out that (dng ) at (λ= 1.3 µm).

This wavelength is referred to as the zero-dispersion wavelength (λZD ),

since (DM = 0) at ( ZD). The dispersion parameter (DM) is negative

below (λZD) and becomes positive above that. It should be stressed that

(λZD = 1.3 µm) only for pure silica. The zero-dispersion wavelength of

optical fibers also depends on the core radius a and the index step

[3].

Figure (2) shows the results obtained after solving Sellmeier

equation for above stated values of the coefficient in (3.1% ) GeO2 doped

silica fiber.

The numerical solution of Sellmeier equation was performed with

Matlab after getting the appropriate values for the defined value of

refractive indices for the fiber under test.

For a conventional single-mode fiber, the zero-dispersion

wavelength shifts to Waveguide dispersion can be used to produce

dispersion- decreasing fibers in which GVD decreases along the fiber

length because of axial variations in the core radius. In another kind of

fibers, known as the dispersion compensating fibers, GVD is made

normal and has a relatively large magnitude[3].

R.S. Habeb

62

Figure (2): Dispersion variation with wavelength

The most notable feature is that (DM) vanish at a wavelength of

about (1.3 μm )and change sign for longer wavelengths, this is shown in

figure (2). This wavelength is referred to as the zero-dispersion

wavelength and is denoted as (λD). However, the dispersive effects do not

disappear completely at( λ = λD). When the input wavelength (λ)

approaches (λD ) to within a few nanometers. The main effect of the

waveguide contribution is to shift (λD) slightly toward longer

wavelengths;( λD ≈ 1.3 μm ) for standard fibers[5].

Sellmeier equation was first showed numerically in order to

estimate the refractive index of both the fiber silica and the group index

for the proposed fiber, as shown in Figure (1). As we can see from the

figure, the refractive index decreased with wavelength, and the required

values at (1.3 μm) were obtained.

Figure (3) shows the variation of dispersion, waveguide, material,

and total as function of wavelength using the OptiFiber package

simulation. In comparison, we can conclude a zero – dispersion fiber at

wavelength 1.3µm.

DW

DM


63

Figure (3): Total Dispersion losses in the fiber

One can see from Figure (3) that the increase of the negative slope

of material dispersion shifts the zero of dispersion towards longer

wavelengths. Thus, the obvious way of dispersion minimum shifting of

transmission is enlarging the influence of the waveguide dispersion. It

can be done by enlargement of difference between the core and the

cladding refraction indices[6].

R.S. Habeb

64

Figure(4): Optical confinement within the fiber by Matlab

Figure (5): Optical confinement within the fiber by "OptiFiber2.0"

Fiber design must fulfill the requirement that the light for the has

must be confined in the core of the fiber. The fulfillment was satisfied in

an proposed fiber by simulation using Matlab for equation (9) and


65

OptiFiber, as shown in figures (4 and 5). As can be noticed from both

figure, the laser light was confined in the core and shows a Gaussian

profile in both diagram.

The modal intensity distribution and the direction of electric fields

is for the fundamental mode as in Figure (4). The fundamental mode is

linearly polarized as indicated by the electric field vectors in Figures.

Figure (6): Variation of group delay with wavelength for its proposed

fiber

The other most important feature of the fiber, is the group

delay(ps/km). This parameter was calculated by using "OptiFiber2.0"for

our proposed fiber. The minimum value of the delay, as can be noticed

from the group, is at (1.3µm) wavelength. the minimum value of this

group delay encourage our suggestion for proposed fiber.

Now, the next step, is to calculated the losses in the proposed fiber,

figure (7), all the losses (hydroxide, infrared, ultraviolet, Rayleigh

scattering ), were the minimum values at (1.3µm) wavelength.

R.S. Habeb

66

Figure (7): Calculation of the losses dependence on wavelength for

the proposed fiber

Figure (8): Image of electric field distribution of the proposed fiber

Figure (8) shows the confinement of fundamental mode and

higher- order modes in the fiber under test. The fundamental mode was

totally confined in the core of diameter (6.728 µm).

4. Conclusion

The concluding remarks that can be outline from the article we as

follows. The proposed fiber working at (1.3µm) with zero – dispersion

and minimum optical material losses were verified. The simulation were

conducted by two numerically parallel methods by solving the equation

Matlab and OptiFiber2.0. Both simulation satisfied our hypothesis for

such a fiber.


67

References:

[1] Ottawa., (2006) ,"OptiFiber 2.0",Computer Aided Design (CAD),

Canada.

[2] Pal, B, P., (2006), "Optical fibers for broadband lightwave

communication : evolutionary trends in designs in Guided

Wave Optical Components and Devices", Elsevier Academic

Press, Burlington and Applications, San Diego, California, USA.

[3] Agrawal., Govind, P., (2002), "Fiber-optic communication

systems", John Wiley and Sons, New York, The Institute of Optics

University of Rochester, 3rd edition.

[4] Chakravarthi, K, M., Watekar, R, P., Babu, V, A., Sateesh, M. Reddy,

V, P., (2012), "Optimization of Silica Glass Micro Fiber for Zero

Dispersion Wavelength", National Conference on Innovative

Paradigms in Engineering and Technology (NCIPET), Proceedings

published by International Journal of Computer Applications

(IJCA)], Chennai, India.

[5] Agrwal., Govind, P., (2007), Nonlinear Fiber Optics, Academic

Press, San Diego, California, 4th edition .

[6] Abramczyk, H., (2005), Introduction to Laser Spectroscopy,

Technical University of Lodz 93-590, Elsevier, Netherlands, 14,

issue 1, www.mitr.p.lodz.pl/evu.

[7] Born , M., Wolf, E., (1999), Principles of Optics, Cambridge

University Press, New York,7th ed.

[8]Quebec , H,L., Varennes, B ,L., (2009), "field (LP01) of a dispersion

shifted fiber at six wavelengths", Canada Photonics Proc, of SPIE ,

7386, 73862C.

[9]Thyagarajan, K,. Pal, B,P,. (2007), "Modeling dispersion in optical

fibers: applications to dispersion tailoring and dispersion

compensation in Optical Fiber Communication Reports",

Ramachandran, S, 4, Springer-Verlag, Berlin.

[10] Jeunhomme, L, B., (1990), Single-Mode Fiber Optics, Marcel

Dekker, New York, 2nd edition.

[11] Abramowitz, M., Stegun, I, A., (1970), Handbook of Mathematical

Functions, Dover, New York.

[12] Dianov, E, M. ,V., Bufetov, I, ,

M., Sazhin, O,D., Prokhorov, A.M., Devyatykh, G,G., Guryanov

A,N and Khopin, V,F., (1998),"Highly efficient 1.3µ m Raman

fiber amplifier", Electron, Lett, 34, 7.

[13] Kyunghwan, O., Choi, S., Jung, Y, S, and Jhang, W, L,. (2005),

"Novel Hollow Optical Fibers and Their Applications in

Photonic Devices for Optical Communications", IEEE J.

Lightwave Techn, 23, 2.

R.S. Habeb

68

[14] Michal ,L.," Photonic Crystal Fibers with Optimized Dispersion

for Telecommunication Systems", Czech Technical University in

Prague, Faculty of Electrical Engineering, Czech Republic.

[15] Tomasz, K., (2008),"Step index fiber modeling to soliton

propagation", Poznańskie Warsztaty Telekomunikacyjne PWT,

Poznań 11.

[16]Kang, Y., (2002),"Calculations and Measurements of Raman

Gain Coefficients of Different Fiber Types", M.Sc. Thesis,

Engineering faculty in Electrical Engineering, Blacksburg, Virginia.

[17] Majewski, A.,1991, Teoria i projektowanie swiatłowodów, WNT,

Warszawa.

design of zero dispersion optical fiber at wavelength 1.3 m

Documents